Taken together, the infinite-dimensional symmetries from soft theorems and the OPE offer new insight into constraints on the organization of scattering data of massless particles [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Notably, they form the basis of an approach to the scattering problem in which the symmetries arising from soft theorems are found to constrain interactions that do not involve any soft particles. Massless particles – irreducible representations of the Poincaré group – are represented by a family of operators of fixed spin and varying boost weight (conformal dimension) \(\Delta \) . In an OPE involving operators of fixed boost weight, the grouping of weights into single-particle families is captured by a non-trivial dependence of the OPE coefficients on the conformal dimensions \(\Delta \)  of the primaries. Standard conformal field theory analysis fixes the OPE up to the coefficients of primary operators, while 4D translations and the symmetries associated to soft theorems relate different conformal families, thereby imposing further constraints on the OPE coefficients.
